Reducing Prediction Error by Transforming Input Data for Neural Networks

The primary purpose of data transformation is to modify the distribution of input variables so that they can better match outputs. The performance of a neural network is often improved through data transformations. There are three existing data transformation methods: (1) Linear transformation; (2) statistical standardization; and (3) mathematical functions. This paper presents another data transformation method using cumulative distribution functions, simply addressed as distribution transformation. This method can transform a stream of random data distributed in any range to data points uniformly distributed on [0,1]. Therefore, all neural input variables can be transformed to the same ground-uniform distributions on [0,1]. The transformation can also serve the specific need of neural computation that requires all input data to be scaled to the range [-1,1] or [0,1]. The paper applies distribution transformation to two examples. Example 1 fits a cowboy hat surface because it provides a controlled environment for generating accurate input and output data patterns. The results show that distribution transformation improves the network performance by 50% over linear transformation. Example 2 is a real tunneling project, in which distribution transformation has reduced the prediction error by more than 13% compared with linear transformation.